Entry details for q = 21 = 2, g = 11
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Lower bound Nmin = 14

 Submitted by Gerrit Oomens Date 01/01/1900 Reference J-P. SerreLetter to G. van der GeerSeptember 1, 1997. Comments Tags Methods from general class field theory

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 Correction S.E.Fischer 12/20/2014 03:42 The extension E/F leads to a curve of genus 4 with 8 points. Extending once again by H of degree 2 leads to the desired result, as we write H/(E/F):= v^2 + v + x^3 + x . Explicit Curve S.E.Fischer 12/18/2014 15:30 We can assume such a curve C as an extension E of degree 2 of a curve F of genus 1 as follows: F: (x + y + x*y) * x*y + x + 1 ; E/F := v^2 + v + x^3 + x . Defining equation Isabel Pirsic 06/18/2012 13:00 (x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*y^8 + (x^10 + x^9 + x^6 + x^5 + x + 1)*y^4 + (x^13 + x^12 + x^11 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2)*y^2 + (x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^6 + x^5)*y + x^21 + x^20 + x^17 + x^15 + x^11 + x^10 + x^8 + x^6
Upper bound Nmax = 14

 Submitted by Everett Howe Date 04/14/2010 Reference Jean-Pierre SerreRational points on curves over finite fieldsNotes by Fernando Q. Gouvêa of lectures at Harvard University, 1985. Comments The Oesterlé bound Tags Oesterlé bound

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